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Abstract:

Several equivariant estimators of multivariate location and scatter are studied, which are highly robust, have a controllable finite-sample efficiency and are computationally feasible in large dimensions. The most frequently employed estimators are not quite satisfactory in this respect. The Minimum Volume Ellipsoid (MVE) and the Minimum Covariance Determinant (MCD) estimators are known to have a very low efficiency. S-estimators with a monotonic weight function like the bisquare have a low efficiency when the dimension p is small, and their efficiency tends to one with increasing p. Unfortunately, this advantage is outweighed by a serious loss in robustness for large p. Four families of estimators with controllable efficiencies whose performance for moderate to large p has not been explored to date are studied: S-estimators with a non-monotonic weight function, MM-estimators, τ-estimators, and the Stahel–Donoho estimator. Two types of starting estimators are employed: the MVE computed through subsampling, and a semi-deterministic procedure previously proposed for outlier detection, based on the projections with maximum and minimum kurtosis. A simulation study shows that an S-estimator with non-monotonic weight function can simultaneously attain high efficiency and high robustness for p≥15, while an MM-estimator with a particular weight function can be recommended for p>15. For both recommended estimators, the initial values are given by the semi-deterministic procedure mentioned above. © 2016 Elsevier B.V.

Registro:

Documento: Artículo
Título:Robust and efficient estimation of multivariate scatter and location
Autor:Maronna, R.A.; Yohai, V.J.
Filiación:Department of Mathematics, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina
Department of Mathematics, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Argentina
Palabras clave:Kullback–Leibler divergence; MM-estimator; S-estimator; Stahel–Donoho estimator; τ-estimator; Multivariable systems; Sampling; Efficient estimation; Equivariant estimators; Minimum covariance determinant; Minimum volume ellipsoids; MM-estimator; Outlier Detection; S-estimators; Simulation studies; Efficiency
Año:2017
Volumen:109
Página de inicio:64
Página de fin:75
DOI: http://dx.doi.org/10.1016/j.csda.2016.11.006
Título revista:Computational Statistics and Data Analysis
Título revista abreviado:Comput. Stat. Data Anal.
ISSN:01679473
CODEN:CSDAD
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_01679473_v109_n_p64_Maronna

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Citas:

---------- APA ----------
Maronna, R.A. & Yohai, V.J. (2017) . Robust and efficient estimation of multivariate scatter and location. Computational Statistics and Data Analysis, 109, 64-75.
http://dx.doi.org/10.1016/j.csda.2016.11.006
---------- CHICAGO ----------
Maronna, R.A., Yohai, V.J. "Robust and efficient estimation of multivariate scatter and location" . Computational Statistics and Data Analysis 109 (2017) : 64-75.
http://dx.doi.org/10.1016/j.csda.2016.11.006
---------- MLA ----------
Maronna, R.A., Yohai, V.J. "Robust and efficient estimation of multivariate scatter and location" . Computational Statistics and Data Analysis, vol. 109, 2017, pp. 64-75.
http://dx.doi.org/10.1016/j.csda.2016.11.006
---------- VANCOUVER ----------
Maronna, R.A., Yohai, V.J. Robust and efficient estimation of multivariate scatter and location. Comput. Stat. Data Anal. 2017;109:64-75.
http://dx.doi.org/10.1016/j.csda.2016.11.006